marlene a. plumlee* a
DESCRIPTION
TRANSCRIPT
Are Information Attributes Priced?
Christine A. Botosan*Associate Professor of Accounting
C. Roland Christensen Faculty FellowEmail: [email protected]
Marlene A. Plumlee* a
Associate Professor of AccountingEmail: [email protected]
*David Eccles School of BusinessUniversity of Utah
Salt Lake City, UT 84112a corresponding author
January 2006
We wish to thank Stephen Brown for his generous assistance in the calculation of the PIN variable used in this study. We also wish to thank the workshop participants at the University College Dublin, University of Utah, New York University, Toronto University, Wharton and University of Wisconsin-Madison for their helpful comments. The authors gratefully acknowledge the financial support of the David Eccles School of Business and the contribution of I/B/E/S Inc. for providing earnings per share forecast data, available through the Institutional Brokers Estimate System. These data have been provided as part of a broad academic program to encourage earnings expectations research.
Are Information Attributes Priced?
Abstract
Easley and O’Hara (EO) (2004) model the impact of information attributes on the cost of equity
capital. We empirically test three implications of the EO model and document results consistent with its
predictions. Specifically we find that cost of equity capital is increasing in the proportion of the
information set that is private versus public, decreasing in the fraction of investors who are informed and
decreasing in the overall precision of the information set. Accordingly we conclude that Easley and
O’Hara’s conjecture that public and private information have a role to play in affecting firms’ required
returns is supported by the data.
1. Introduction
Easley and O’Hara (EO) (2004) model the impact of information attributes on the cost of equity
capital. They conclude that cost of equity capital is affected by the following attributes of information: (1)
the proportion of the information set that is private versus public (hereafter composition), (2) the fraction
of investors who are informed (hereafter dissemination), and (3) the overall precision of the information
set (hereafter precision). EO demonstrate that cost of equity capital is increasing in the composition of the
information set and decreasing in its dissemination and precision. We empirically test these three
implications of the EO model and document results consistent with the model’s predictions.
We employ two alternative proxies for the cost of equity capital – rDIVPREM and rPEGPREM. rDIVPREM is
derived from the dividend discount model and is the internal rate of return that equates a firm’s current
stock price to analysts’ forecasts of future dividends and target price (Botosan and Plumlee (2002);
Botosan et al. (2004)). rPEGPREM is similarly derived from the dividend discount model, but after imposing
the assumption that both dividends prior to the earnings forecasts and growth in abnormal earnings
beyond the forecast horizon are zero (Ohlson and Juettner-Nauroth (OJ) (2003); Easton (2004)). Botosan
and Plumlee (2005) assess the empirical validity of five alternative methods of estimating cost of equity
capital including rDIVPREM and rPEGPREM and conclude that, among those examined, only these estimates are
predictably and robustly related to risk.1
Our proxies for the composition and precision of information are drawn from Barron et al. (BKLS)
(1998). BKLS demonstrate how observable attributes of analysts’ forecasts can be employed to estimate
the precision of the analysts’ public and private information sets. We employ these measures to derive
estimates of the overall precision of the information set (labeled PRECIS), and the proportion of the
information set that is private versus public (labeled COMPOS). We compute a proxy for the fraction of
1 For other research that examines possible proxies for expected cost of equity capital see Botosan (1997), Gebhardt
et al. (2001), and Gode and Mohanram (2003).
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investors who are informed (labeled DISSEM) using the estimated arrival rates of informed and
uninformed investors, both of which are components of the probability of an informed investor (i.e. PIN)
metric developed in Easley et al. (1997).
We find that both proxies for cost of equity capital are increasing in COMPOS and decreasing in
DISSEM and PRECIS, consistent with the EO model and EO’s conjecture that information attributes are
priced. The magnitudes of our coefficients suggest that an increase in COMPOS of 10 points (e.g. from
20% to 30%) is associated with an increase in cost of equity capital of about 7 basis points, whereas a
similar increase in DISSEM is associated with a decrease in cost of equity capital of about 38 basis
points, on average. In addition, the sample firm providing the most precise information enjoys a cost of
equity capital that is 114 basis points lower than the sample firm providing the least precise information.2
One implication of our findings is that managers can realize a lower cost of equity capital by reducing
private information relative to public information. Most existing research (including the EO model)
assumes that public information supplants private information, which suggests that managers might
realize cost of equity capital benefits by providing more public disclosures. However, a relatively early
stream of research suggests that some types of public disclosure might generate private information (see
Barron et al. (2005), and Botosan et al. (2004)), indicating that further research is needed to help
managers evaluate their optimal reporting strategy. Another implication of our findings is that managers
can procure lower costs of equity capital by adopting corporate reporting strategies that mitigate
investors’ costs of becoming informed thereby encouraging greater dissemination of private information.
For example, managers might increase the transparency of their disclosures to reduce investors’
information processing costs. Managers might also hold conference calls or host analyst “road-shows” to
encourage a greater analyst following. Finally, managers can achieve cost of equity capital benefits by
choosing accounting policies and disclosure practices that increase the overall precision of information.
Our study contributes to a growing body of empirical literature which focuses on the association
between information and cost of equity capital. For example, several papers examine the relationship
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between corporate financial reporting practices and cost of equity capital (see Botosan (1997), Botosan
and Plumlee (2002), Brown et al. (2004), and Richardson and Welker (2001)). In addition, a number of
papers relate attributes of earnings to cost of equity capital (see Affleck-Graves et al. (2002), Francis et al.
(2004), Hribar and Jenkins (2004), and Mikhail et al. (2004)). Common to all of these studies is a focus
on public information. Two more recent studies focus on proxies for private information and so are most
closely related to this endeavor. First, Botosan et al. (BPX) (2004) show that rDIVPREM is increasing in the
precision of private information, but decreasing in the precision of public information. Second, Easley et
al. (EHO) (2002) document a positive association between realized returns and PIN, their proxy for
COMPOS.
Our paper extends this stream of research in general and the research conducted by BPX and EHO in
particular, in several respects. First, BPX focus on the separate impacts of public and private information
precision on cost of equity capital, whereas our study considers the relationship between overall precision
and cost of equity capital in tandem with proxies for composition and dissemination. Second, EHO
employ realized returns for cost of equity capital. In contrast we employ measures of implied cost of
equity capital in the analysis. Third, ours is the first study to consider the relationship between cost of
equity capital and all three of the information attributes suggested by the EO model.
We organize the remainder of our paper as follows. We outline the theory that underlies our
hypotheses and discuss prior research related to this study in Section I. We describe our research design
and empirical proxies in Section II, and our sample and descriptive statistics in Section III. We present the
results of our analysis in Section IV, and Section V concludes the paper.
2. Hypotheses development and prior research
2.1. Hypotheses development
Easley and O’Hara (2004) (EO) develop a multi-asset, rational expectations, equilibrium asset-pricing
model that incorporates public and private information, as well as informed and uninformed risk-averse
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investors. Within this framework EO consider the impact of cross-sectional differences in (1) the
composition of information between public and private information, (2) the dissemination of private
information across traders, and (3) the overall precision of information on firms’ costs of equity capital.3
In the EO model uninformed investors perceive stocks to be risky due to information risk and demand
higher returns to compensate for this additional risk. In contrast, informed traders perceive less
information risk and, therefore, are willing to take larger positions in securities about which they are
informed. Trading by informed investors can have two beneficial effects on the firm’s cost of equity
capital. First, since informed investors take larger positions in the firm’s stock, demand for the firm’s
securities may be increased thereby reducing the cost of equity capital. Second, uninformed investors
partially infer private information from stock price; they perceive less information risk when the trading
activities of informed investors reveal their private information with greater precision.
The impact of the composition, dissemination, and precision of information on cost of equity capital
results from the interplay among the effects outlined above. With respect to the composition of the
information set, EO demonstrate that stocks with more private information and less public information
face a higher cost of equity capital. This is because uniformed investors can not perfectly infer private
information from stock price, such that firms with relatively more private information are viewed as more
risky by uninformed investors and are charged a higher cost of equity capital as a result. This gives rise to
our first hypothesis, stated below.
H1: Cost of equity capital is increasing in the proportion of information that is private.
With respect to the dissemination of information, EO demonstrate that when private information is
more widely disseminated across investors, cost of equity of capital is reduced via the demand effect and
the information revelation effect. First, when more investors are informed, demand for the stock is
greater, price is higher, and cost of equity capital is lower. Second, when more investors are informed
their private information is revealed to uninformed investors with greater precision. This makes the stock
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less risky for uninformed traders and further reduces the cost of capital. This gives rise to our second
hypothesis.
H2: Cost of equity capital is decreasing in the dissemination of private information across investors.
With respect to the overall precision of information, EO demonstrate that greater precision lowers cost
of equity capital by making the stock less risky for the uninformed investors. Uninformed investors
perceive less information risk because the public information they observe directly and the private
information revealed to them indirectly via stock price are both more precise. This gives rise to our third,
and final, hypothesis.
H3: Cost of equity capital is decreasing in the overall precision of information.
2.2. Prior Research
A large body of empirical research investigates the association between public information and cost of
equity capital. One segment of this research broaches this issue indirectly by examining the effect of
disclosure on variables believed to be related to cost of equity capital. For example, Frankel et al. (1995)
find that managers of firms that access the capital markets provide management earnings forecasts more
frequently. Welker (1995) and Leuz and Verrecchia (2000) document a negative association between
disclosure levels and bid-ask spreads. Healy et al. (1999) find that firms that increase disclosure
experience an increase in stock performance, institutional ownership, and analyst following, and a
decrease in bid-ask spreads. Brown et al. (2004) find that a policy of regularly holding conference calls
mitigates information asymmetry. Finally, Affleck-Graves et al. (2002) demonstrate a favorable
association between earnings predictability and reduced information asymmetry.
Another segment of this research broaches the association between public information and cost of
equity capital by examining the effect of disclosure on the cost of raising equity capital via a secondary
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offering or on estimates of cost of equity capital. For example, Lang and Lundholm (2000) conclude that
hyping a stock in anticipation of a secondary offering increases price and allows the firm to raise capital
at a lower cost. Botosan (1997) finds that among firms with low analyst following, greater annual report
disclosure is associated with a lower cost of equity capital and Botosan and Plumlee (2002) extend this
result to large, heavily followed firms. Finally, several recent papers document a negative association
between earnings “quality” and cost of equity capital (e.g. Francis et al. (2004), Hribar and Jenkins
(2004), and Mikhail et al. (2004)).
All of the research discussed above focuses on public information. Two more recent studies, Botosan
et al. (2004) (BPX) and Easley et al. (2002) (EHO), consider the effects of public and private information
on cost of equity capital, and, as such, are most closely related to this study. BPX use separate empirical
proxies for the precision of public and private information to examine the effect of private information
precision on cost of equity capital, after controlling for the negative association between cost of equity
capital and public information established in the prior literature. BPX find that cost of equity capital is
increasing in the precision of private information and that the precision of private information is
positively correlated with the precision of public information. They find that, for the average firm, the
cost of capital reduction achieved through more precise public information is almost entirely offset by the
cost of capital increase associated with more precise private information.
BPX consider the precision of private and public information as separate constructs. While the EO
model allows the precisions of private and public information to differ, the model is silent as to the
separate effects of each of these precisions on cost of equity capital. Moreover, BPX’s finding of a
positive correlation between the precisions of private and public information is not consistent with EO’s
assumption that the precisions of private and public information are perfect substitutes. BPX do not
examine the effect of overall precision or dissemination of information on cost of equity capital, nor do
they examine the impact of composition in tandem with precision or dissemination.
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EHO test the hypothesis put forward in EO regarding the composition of information. Consistent with
the EO model, EHO document a strong positive association between realized returns, their proxy for the
cost of equity capital, and PIN, their proxy for the fraction of information that is private. But, prior
research suggests that realized returns are not a powerful proxy for cost of equity capital when sample
size is limited in large part because “information about future cash flows is the dominant factor driving
firm-level stock returns” (Voulteenaho (2002)).
This may explain why EHO find no association between cost of equity capital and beta and book-to-
price and a positive association with firm size. Moreover, EHO’s PIN proxy for composition might also
capture dissemination. This is a significant issue because composition and dissemination have opposite
effects on cost of equity capital in the EO model. Finally, EHO focus on one information attribute –
composition. If composition, dissemination and/or precision are correlated, including one attribute in the
analysis without controlling for the other attributes may result in a correlated omitted variables bias.
Our study complements and extends existing research by (1) employing implied cost of equity capital
estimates in the analysis, (2) employing an alternative proxy for composition that is suggested by the EO
model, and (3) examining all three information attributes simultaneously.
3. Research design and empirical proxies
3.1. Empirical model
To examine the relationship between cost of equity capital and the composition, dissemination and
precision of information we estimate the following regression equation.
(1)
Where: rit = equity risk premium (i.e. cost of equity capital less the risk free rate) for firm i, year t. BETAit = market model beta for firm i, year t.
LGROWit = log of long range expected growth in earnings, year t.LMKVLit = log of market value of common equity for firm i, year t.BPit = book-to-price for firm i, year t.COMPOSit = percentage of total precision attributed to private information for firm i, year t.
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DISSEMit = percentage of trades by informed traders. PRECISit = total information precision for firm i, year t.
Based on the theory set forth in EO, we hypothesize that the coefficient on COMPOS (γ5) is positive,
and the coefficients on DISSEM (γ6) and PRECIS (γ7) are negative.
We include market beta, growth, firm size, and book-to-price in the analysis to control for other
sources of risk that could confound our analysis, and to validate our proxy for cost of equity capital. We
expect the coefficient on BETA to be positive since the Capital Asset Pricing Model indicates that cost of
equity capital is increasing in market beta.4 Beaver et al. (1970) argue that abnormal earnings streams
derived from growth opportunities are more risky and La Porta (1996) provides empirical evidence that
growth and risk are positively related. Accordingly we expect to observe a positive coefficient on
LGROW. Berk (1995) argues that, market value of equity (book-to-price) is inversely (positively)
associated with risk in general, and that cost of equity capital is negatively related to market value of
equity and positively related to book-to-price in an incomplete model of expected returns. Thus, we
expect the coefficient on LMKVL to be negative and the coefficient on BP to be positive. The procedures
we employ in estimating our variables are described in detail below.
3.2. Empirical proxies – cost of equity capital and control variables
3.2.1. Cost of equity capital (rDIVPREM and rPEGPREM)
The dependent variable in our model is the expected risk premium, or cost of equity capital net of the
risk free rate of interest. Botosan and Plumlee (2005) evaluate the construct validity of five popular
methods of estimating firm-specific cost of equity capital and find that the target price method and the
price-earnings-growth (PEG) method generate estimates (rDIVPREM and rPEGPREM, respectively), which are
consistently and predictably related to risk, while the alternative methods do not. Based on their results,
BP conclude that researchers requiring firm-specific estimates of expected cost of equity capital are
4 See Litner (1965), Mossin (1966) and Sharpe (1964).
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justified in using either rDIVPREM or rPEGPREM to proxy for cost of equity capital. To assess the robustness of
our results to the proxy employed, we estimate cost of equity capital using both methods.
The target price method estimates the internal rate of return that equates current stock price to the
present value of forecasted dividends and target price. It employs the short-horizon form of the dividend
discount formula given in equation (2). In this specification of the dividend discount model the forecasted
terminal value truncates the infinite series of future cash flows at the end of year 5.
(2)
Where: = price at time t=0 or t=5. rDIV = estimated cost of equity capital.
= the expectations operator.
= dividends per share, t=1 to 5.
The data and procedures we employ in estimating rDIV mirror those employed by Botosan and Plumlee
(2005). Dividend forecasts for the current fiscal year (i.e., t=1), the following fiscal year (i.e., t=2), the
long run (i.e., t=5), and maximum and minimum long-run target price estimates are collected from
forecasts published by Value Line during the third quarter of the calendar year. These data are collected
from the Value Line database, available in machine-readable form.
Value Line does not provide dividend forecasts for years 3 and 4. Accordingly, we assume linear
growth in dividends from year 2 to year 5, and interpolate between these years to generate dividend
forecasts for years 3 and 4. Forecasted target price is the 50th percentile of Value Line’s forecasted long-
run price range. Current stock price (P0) equals the stock price reported on CRSP on the Value Line
publication date or closest date thereafter within 3 days of publication.
We use the values for P0, E0[P5] and the E0[dt]’s (t=1 to 5) in a numerical approximation program that
identifies the annual firm-specific rDIV that equates the right and left-hand sides of the equation to within a
$0.005 difference between the actual- and fitted-value of P0.5 rDIVPREM is rDIV less the risk free rate of
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interest. We use the 5-year Treasury Constant Maturity Rate as of the end of the month in which the
expected cost of equity capital estimates are determined as our estimate of the risk free rate of interest.
We collect these data from the US Federal Reserve at www.federalreserve.gov.
The primary assumption underlying this method is that analysts’ forecasts of future dividends and
target prices accord with those of market participants. If this assumption is violated, the link between
current stock price and analysts’ forecasts of future cash flows is strained and the link between the
resulting estimates of cost of equity capital and the underlying construct is weakened. This mitigates
against finding results.
Since cost of equity capital is inherently unobservable and Botosan and Plumlee (2005) conclude that
the PEG method also produces estimates that behave as if they capture cross-sectional variation in cost of
equity capital, we triangulate our analysis by examining the estimates produced by the PEG method as
well. Accordingly, our second estimate of cost of equity capital is based on the formula below, drawn
from Easton (2004).
(3)
Where: rPEG = estimated cost of equity capital. E0 = the expectations operator.epst = earning per share at time t.
This formula is derived from a special case of the dividend discount model that assumes no changes in
abnormal earnings beyond the forecast horizon, and no dividend payments prior to the earnings forecasts.
Consistent with Botosan and Plumlee (2005), we use long-run earnings forecasts (eps5 and eps4) in place
of eps2 and eps1 in the above model for two reasons. First, in some instances eps2 is less than eps1, but in
no instance is eps5 less than eps4. Since we cannot solve the model if eps2 is less than eps1 using eps5 and
eps4 maximizes our sample size. Second, and more importantly, using long-run earnings forecasts
increases the likelihood that changes in abnormal earnings beyond the forecast horizon will equal zero.
rPEGPREM is rPEG less the risk free rate of interest.
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3.2.2 Market beta (BETA)
Market beta is estimated using the market model with a minimum of 30 out of 60 monthly returns and
a market index return equal to the value weighted NYSE/AMEX return. We obtain the data to estimate
BETA from CRSP. The estimation period for BETA ends on June 30th of the year cost of equity capital is
estimated.
3.2.3. Long-term growth in earnings (LGROW)
Our estimate of long-range growth in earnings is the 3-5 year annual rate of change in expected
earnings included in the Value Line database.6 We use a natural log transformation of the data to mitigate
skewness in the distribution of long- range growth in earnings.
3.2.4. Market value of equity (LMKVL)
We compute market value of equity by multiplying the number of common shares outstanding by
stock price at the quarter-end immediately prior to June 30th of the year cost of equity capital is estimated.
We draw these data from the quarterly Compustat tape. If these data are unavailable, we substitute the
market value of the firm reported on CRSP as of June 30th of the Value Line publication year. Market
value of equity is stated in millions of dollars. We use a natural log transformation of the data to mitigate
skewness in the distribution of market value of equity.
3.2.5. Book-to-price (BP)
We compute book-to-price by scaling the book value of the firm’s common equity by its market value.
Both the numerator and the denominator of the ratio are measured at the quarter-end immediately prior to
June 30th of the year cost of equity capital is estimated. We collect these data from the quarterly
Compustat tape. If these data are unavailable, we substitute data for the fiscal year-end immediately prior
to June 30th of the year cost of equity capital is estimated. These data are collected from the annual
Compustat tape.
3.3. Empirical proxies – attributes of information
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3.3.1. Composition
In the EO model, composition is measured by k, the fraction of stock k’s information set that is
private. We cannot observe k directly. However, it can be shown that k is equal to the precision of
private information divided by the sum of the precision of private and public information. In EO’s model
the precision of private information is given by kIkk, where k is the number of signals in the
information set and k is the precision of the distribution from which the public and private signals are
drawn. Further, the precision of public information is given by (1-k)Ikk. Accordingly, it is
straightforward to demonstrate that k equals the ratio of private precision to private plus public precision
as given by equation (4) below.
(4)
Our proxy for the fraction of information that is private (COMPOS) is based on equation (4). We
substitute the precision of private (PRIVATE) and public (PUBLIC) information measures derived by
Barron et al. (BKLS) (1998) for kIkk and (1-k)Ikk, respectively in equation (4). Accordingly,
COMPOS is given by equation (5) below.
(5)
3.3.2. Estimating PRIVATE and PUBLIC
BKLS demonstrate how observable properties of analysts’ forecasts (squared error in the mean
forecast, forecast dispersion and the number of analysts providing forecasts) can be used to infer
unobservable attributes of analysts’ information environment. In their analysis BKLS make the following
assumptions: (1) analysts observe a signal common to all analysts (i.e. the public signal); (2) each analyst
also observes a signal unique to the individual analyst (i.e. the private signal); and (3) analysts’ forecasts
of earnings are unbiased and are based only on their public and private signals.
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Given these assumptions, BKLS show how error in analysts’ public and private information sets is
reflected differently in the squared error in the mean forecast and forecast dispersion. Specifically, error
arising from analysts’ reliance on public information is fully reflected in the squared error in the mean
forecast, while idiosyncratic error arising from analysts’ reliance on private information is captured only
to the extent that it is not diversified away by the process of averaging across analysts. In contrast,
forecast dispersion reflects idiosyncratic error only. BKLS further demonstrate that when the precision of
private information is similar across analysts, squared error in the mean forecast and forecast dispersion
can be expressed as functions of the precision of public and private information.
With this structure in place, BKLS begin by defining observable variables (squared error in the mean
forecast and forecast dispersion) in terms of unobservable constructs (the precision of public and private
information). BKLS then reverse these relationships to solve for unobservable public and private
information precision in terms of the observable variables. The resulting formulas derived by BKLS for
the precision of public and private information are given by equations (6) and (7), respectively.
(6)
(7)
Where: SE = squared error in the mean forecast.
D = forecast dispersion.
N = number of forecasts.= mean forecast for firm i, quarter t.
Ait = actual earnings for firm i, quarter t.Fijt = analyst j’s forecast of earnings for firm i, quarter t.
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We estimate SE, D, and N quarterly using analysts’ most recent one-quarter-ahead forecasts of
quarterly earnings. We collect forecast and actual earnings data from IBES. A minimum of three
individual analysts must provide forecasts of earnings for a given firm-quarter for that firm-quarter to be
included in our sample. To obtain our final measures of the precision of public and private information,
we take a time-series average of the four successive quarterly values of PUBLIC and PRIVATE that
precede the third quarter of the calendar year in which rDIVPREM and rPEGPREM are estimated. This generates
an estimate of the average level of precision of public and private information for each firm, for each
year. Since PUBLIC and PRIVATE are, in theory, the inverse of the variance of analysts’ public and
private information signals, non-negative values of PUBLIC and PRIVATE are not meaningful.
Consistent with prior research, we limit our analyses to non-negative values of PUBLIC and PRIVATE.
Barron et al. (2002) conduct extensive analyses to investigate the sensitivity of their results to
violations of the BKLS assumptions with no impact on their conclusions. Venkataraman (2000) conducts
similar analyses, also with no impact on his conclusions. Moreover, the measures developed by BKLS are
employed in a number of prior empirical studies including Barron et al. (1999), Venkataraman (2000),
Botosan and Harris (2000), Barron et al. (2002), Byard (2001), Byard and Shaw (2002), and Botosan et
al. (2004). Accordingly, we believe that the BKLS assumptions are sufficiently descriptive to render the
BKLS measures useful in empirical research.
While the measures derived by BKLS use observable properties of analyst forecasts to assess the
underlying attributes of analysts’ information environment, Barron et al. (BHS) (2005) find that investors’
trade volume responses to quarterly earnings announcements are predictably associated with changes in
analysts’ information environment estimated with the BKLS measures. Thus, BHS conclude that the
BKLS measures are a good proxy for investors’ information environment with respect to a given firm. If
this assumption is not valid and the characteristics of analysts’ information environment differ from those
of investors, PUBLIC and PRIVATE represent noisy measures of the underlying constructs we seek to
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capture. While this measurement error may mitigate against finding results, we do not expect it to induce
bias.
3.3.2. Dissemination
We use the proportion of informed traders to total traders as our proxy for the fraction of investors
who are informed (DISSEM). We derive the inputs into DISSEM from the PIN measure developed in
Easley et al. (EKO) (1997). 7 EKO model a market maker’s beliefs as a function of α (the probability of an
information event), δ (the probability the new information is bad news), μ (the arrival rate of informed
traders), εb (the arrival rate of uninformed buyers), and εs (the arrival rate of uninformed sellers). In brief,
the EKO model interprets a normal level of buys and sells as uninformed trades, which allows for
estimates of the arrival rate of uninformed traders (εb and εs). Abnormal buy or sell order volume is
considered information-based trading and is used to estimate the arrival rate of informed traders (μ). The
number of days on which there is abnormal buys or sells is used to identify both the probability of an
information event (α) and the probability the news is bad (δ).
We estimate buys and sells using TAQ data and the Lee-Ready algorithm known as the tick test (Lee
and Ready (1991)). Then, using a maximum likelihood procedure, we estimate the parameters of the
model (α, δ, μ, εb, and εs) simultaneously. We use the estimates of μ, εb, and εs produced by this procedure
to compute our measure of dissemination.
Different researchers have adopted different methods to deal with the truncation error that arises when
one attempts to estimate the parameters of PIN with a large number of daily buys and sells. For example,
Easley et al. (2001) (EEOW) set the arrival rate of uninformed buyers and sellers equal to each other (i.e.
εb = εs = ε) and factor out a common factor to simplify the log likelihood function and mitigate the
problem. In contrast, Vega (2004) allows εb and εs to differ, but she alters the form of the log likelihood
7 In prior research, PIN is used as a proxy for the risk of information based trading (Easley et al. (1996a)), the
probability of information based trading (Easley et al. (1996b)), a measure of information asymmetry (Brown et al.
(2001)), and a measure of the composition of the information set (Easley et al. (2002)).
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function to mitigate truncation error. For completeness, we estimate the parameters using the empirical
methods employed by EKO, EEOW and Vega. Empirically, we find that the estimates from the three
methods are highly correlated (on average, the correlations exceed 0.70). We use the parameter estimates
from EEOW (2001) in equation (8) to estimate DISSEM, because the EEOW method results in the largest
number of observations.8
DISSEM = (8)
3.3.3. Precision
Our proxy for the overall precision of information for a given firm (PRECIS) is computed by
taking the sum of the PUBLIC and PRIVATE estimates described previously. Consistent with the notion
that PRECIS captures the quality of the overall information set, BKLS refer to this sum as a measure of
informedness.
4. Sample selection and descriptive statistics
4.1. Sample selection
Our sample consists of 3,896 firm/year observations from 1993-2003. Observations are included in the
sample if we have sufficient data from Value Line, IBES, Compustat, CRSP, and TAQ to estimate the
variables described above. The number of observations varies by year and increases across time except
for the last two years of the sample period where we lose more observations due to truncation error
because the number of daily buys and sells is larger in these years than in earlier years.
4.2. Descriptive statistics
Table I provides descriptive statistics pertaining to our cost of capital estimates and independent
variables. We compute our descriptive statistics using all observations in our sample pooled across the
years 1993-2003. The mean (median) values of our estimates of the risk premium are 9.2% (7.8%) for
rDIVPREM and 5.7% (4.9%) for rPEGPREM. In comparison, Botosan and Plumlee (2005) employ a sample
spanning 1983 through 1993 and estimate mean (median) values of 6.4% (5.7%) for rDIVPREM and 5.0%
18
(4.4%) for rPEGPREM. Our rDIVPREM estimates exceed those reported in BP because we use the 50th percentile
of Value Line’s forecasted long-run price range whereas BP use the 25th percentile.9
Mean (median) BETA for our sample is approximately 1.02 (0.94). These data indicate that our
average (median) sample firm presents a level of market risk slightly greater (lower) than that of the
market portfolio. Mean (median) expected long-term growth in earnings (GROW) is 14.2% (12.3%).
These growth statistics are similar, albeit lower, than the 15.1% mean and 13.7% median long-term
growth in IBES earnings documented by Gode and Mohanram (2003) for an earlier time period. Mean
MKVL is $6893.8 million; the median is $1915.8 million, which indicates a sample populated by
relatively large firms and a skewed distribution. Mean (median) book-to-price (BP) equals 0.47 (0.41),
indicating that our sample is characterized by firms trading at a substantial premium above book value.
This is consistent with the relatively high rate of growth noted earlier.
COMPOS is 0.21 at the mean (0.05 at the median), suggesting that approximately 21% of the
information set for our average sample firm is comprised of private information. The interquartile range
of COMPOS is large, ranging from 0.00 at the 25th percentile to 0.36 at the 75th percentile. DISSEM has a
mean (median) value of 0.31 (0.30), which suggests that the average firm has approximately 31%
informed traders. Based on data presented graphically in Easley et al. (EHO) (2002), we estimate that in
the final year of their sample period (i.e. 1998), EHO’s mean values of μ, εb, and εs, are approximately
52%, 48% and 46%, respectively, suggesting a value of DISSEM of approximately 36%. This value lies
within the interquartile range of our data, which is approximately 24% at the 25th percentile and 37% at
the 75th percentile.10 Finally, the mean (median) value for PRECIS is 3296.8 (2166.9). The distribution of
PRECIS is skewed and has a large interquartile range – 684.8 at the 25th percentile and 5121.7 at the 75th
percentile. Consistent with prior empirical research employing the BKLS measures of the precision of
public and private information, we overcome the problem of skewness in the data by using the fractional
rank of PRECIS (RPRECIS) in our analysis.
19
Insert Table I here.
5. Empirical Results
5.1. Rank correlation among risk premium estimates and independent variables
Table II presents correlation statistics among our estimates of the risk premium and our independent
variables. To mitigate the impact of outlying observations we examine Spearman correlation coefficients.
The values reported in Table II represent the average of the year-by-year correlation coefficients across
the eleven years included in our sample. The values reported in parentheses are the number of years out of
the eleven sample years that the correlation between the variables is significantly positive/negative.
Consistent with prior research in this area, Table II documents a strong positive correlation between
rDIVPREM and rPEGPREM (0.68). This result indicates that these variables are related to the same underlying
construct. In addition, both rDIVPREM and rPEGPREM are positively correlated with the control variables
BETA, LGROW, and BP and negatively correlated with LMKVL. Similar to findings documented in
Botosan and Plumlee (2005), the correlation between rPEGPREM and the control variables is stronger than
with rDIVPREM, although the signs are the same. The correlations we document are consistent with theory
and suggest that our proxies capture required returns.
The univariate correlations between rDIVPREM and rPEGPREM and COMPOS are positive, as expected.
COMPOS is positively related to rDIVPREM in nine of eleven years and to rPEGPREM in eight years. The
univariate correlation between rDIVPREM and rPEGPREM and DISSEM is positive, which is contrary to our
expectations. However, DISSEM is highly negatively correlated with firm size, which is itself negatively
correlated with cost of equity capital, making it difficult to disentangle the effects using univariate
analysis. Finally, the univariate correlations between RPRECIS and rDIVPREM and rPEGPREM are negative as
expected. RPRECIS is significantly negatively related to rDIVPREM in four years and to rPEGPREM in nine
sample years.
20
Among our explanatory variables of interest we find that COMPOS is negatively related to RPRECIS
(ρ= - 0.359). This is not surprising given the manner in which the variables are computed. COMPOS is
positively related to DISSEM (ρ=0.127), which suggests that when a greater proportion of the
information set is private, private information is held by a greater proportion of the investor set. Finally,
there is a negative correlation between RPRECIS and DISSEM, which suggests that firms with less
precise information tend to have a greater proportion of informed investors.
All three of our explanatory variables, COMPOS, DISSEM and RPRECIS, are correlated with
LMKVL and BP, but we document a particularly strong correlation between DISSEM and LMKVL (ρ= -
0.793). This latter finding is consistent with prior research employing PIN (e.g., Easley et al. (2002) and
Brown et al. (2001)). The strength of this relationship raises the possibility of multicollinearity, which
could hamper our ability to document statistically significant results. In addition, DISSEM is positively
correlated with LGROW in nine of our eleven sample years.
In summary, our univariate correlation results provide support for the following preliminary
conclusions. First, rDIVPREM and rPEGPREM perform well in capturing cross-sectional variation in risk. Second,
we find evidence that cost of equity capital is related to the composition and precision of information, as
predicted by the EO model, but no evidence of the anticipated negative association between cost of equity
capital and dissemination. However, significant correlations among the explanatory and control variables
emphasize the need to examine the relationship between cost of equity capital and the attributes of
information in a multivariate setting.
Insert Table II here.
5.2. Regression of expected cost of equity on control variables and information attributes
Table III presents the results of estimating regression equation (1). Panel A reports the results with
rDIVPREM as the dependent variable. The parameter values reported in the table are the average parameter
values from eleven annual regressions with adjusted Fama-MacBeth t-statistics shown in parentheses. In
21
computing the t-statistics, we weight the coefficients by the square root of the annual sample size to
adjust for differences in the number of observations per year, and we adjust for autocorrelation in the
annual coefficients based on an AR(1) autocorrelation structure by multiplying the standard errors by an
adjustment factor, , where n is the number of years (11) and is the first-order
autocorrelation of the annual coefficient estimates (Abarbanell and Bernard, 2000).
The association between rDIVPREM and each of the control variables is consistent with our expectations.
Specifically, rDIVPREM is increasing in market beta and growth, and decreasing in market value of equity.
The coefficient on book-to-price is not statistically significant when LMKVL is included in the regression
equation, but it is significantly positive when LMKVL is removed from the analysis. These findings are
consistent with BP and LMKVL serving a similar role in the regression equation – that of capturing risk
in general when included in an incomplete model of expected returns.
rDIVPREM is increasing in COMPOS (coefficient of 0.007) and decreasing in DISSEM (coefficient of –
0.121) and RPRECIS (coefficient of – 0.010). Each of the coefficients is statistically significant at a p-
value less than 5%. These results suggest that cost of equity capital is higher when a greater proportion of
the information about a firm is private, but lower when private information is more widely disseminated
across investors and when the information set is more precise. In results not tabled, we document a 7.6%
increase in the overall explanatory power of the regression when COMPOS, DISSEM, and PRECIS are
added to the model.
Panel B reports our results from estimating the regression equation with rPEGPREM as the dependent
variable. These results are similar to those reported in panel A – COMPOS, DISSEM, and RPRECIS as
well as the control variables are related to rPEGPREM as predicted.
In summary, our results support the predictions drawn by EO from their model in three respects. First,
all else equal, firms with a higher proportion of private information face a higher cost of equity capital.
Second, all else equal, firms enjoy a lower cost of equity capital when private information is more widely
22
disseminated across investors. Finally, firms with greater overall information precision also enjoy a lower
cost of equity capital.
6. Conclusion
We test three hypotheses related to the impact of information attributes on the cost of equity capital as
suggested by the model developed in Easley and O’Hara (2004). According to EO’s model (1) firms with
a greater proportion of private information face a higher cost of equity capital; (2) firms with more widely
disperse private information face a lower cost of equity capital; and (3) firms with greater information
precision also face a lower cost of equity capital. We regress two alternative measures of expected cost of
equity capital on proxies for these three information attributes and document results consistent with all
three hypotheses.
Our results suggest that managers might take actions that impact the composition, dissemination and
precision of their firm’s information set to achieve a lower cost of equity capital. For example, managers
might realize cost of equity capital benefits by providing greater public disclosure to reduce the share of
the information set that is private. Alternatively, managers might hold conference calls, host road-shows,
increase the transparency and availability of their disclosures, or take other actions to reduce investors’
information acquisition and processing costs and encourage greater dissemination of private information.
Finally, managers might achieve cost of equity capital benefits by choosing accounting policies and
disclosure practices that increase the overall precision of information.
A key assumption underlying much of the existing theoretical research that relates information to cost
of equity capital is that the precision of public information and the precision of private information are
inversely related. Even so, a relatively early stream of research suggests that some types of public
disclosure might generate private information (see Barron et al. (2005), and Botosan et al. (2004)). These
early findings are important because an inverse relationship is critical to managers’ ability to favorably
impact their cost of equity capital through greater public disclosure. In the absence of such a relationship,
23
the identification of a firm’s optimal disclosure policy is a much more complex problem than suggested
by the results presented herein. Given the important role cost of equity capital plays in the allocation of
resources among firms in the economy and among projects within a firm, additional research focused on
this issue is warranted.
24
Table 1Descriptive statistics for the period 1993-2003a
Variable Mean Std. Dev. 25%
50% 75%
rDIVPREM 0.092 0.082 0.037 0.078 0.128rPEGPREM 0.057 0.043 0.032 0.049 0.072BETA 1.020 0.557 0.666 0.943 1.275GROW 0.142 0.084 0.096 0.123 0.162MKVL 6893.8 19571.0 792.9 1915.8 5131.1BP 0.465 0.355 0.259 0.407 0.593COMPOS 0.208 0.279 0.000 0.054 0.360DISSEM 0.311 0.065 0.238 0.302 0.374PRECIS 3296.8 3142.0 684.8 2166.9 5121.7
a rDIVPREM is the estimated risk premium based on the target price method (BP 2005). rPEGPREM is the estimated risk premium based on the PEG method (Easton 2004). BETA is capital market beta estimated via the market model with a minimum of 30 monthly returns over the 60 months prior to June 30th of the year expected cost of equity capital is estimated using a value weighted NYSE/AMEX market index return. GROW is the Value Line long-range earnings growth forecasts. MKVL is the market value of equity as of the most recent quarter prior to the date cost of equity is calculated, stated in millions of dollars. BP is the book value of common equity scaled by the market value of common equity, both measured at the end of the most recent quarter prior to June 30th of the year cost of equity capital is estimated. COMPOS is the proportion of overall precision attributed to private information measured as PRIVATE/(PUBLIC + PRIVATE), where PUBLIC is the precision of analysts’ public information set and PRIVATE is the precision of analysts’ private information set, both based on the BKLS method. DISSEM is the dissemination of private information across traders measured the number of informed traders (μ), scaled by the sum of the informed and uninformed traders (μ+2), drawn from the calculation of PIN (EEOW (2001)). PRECIS is total information precision calculated as PUBLIC + PRIVATE. The table contains means, medians, 25th percentiles, 75th percentiles, and standard deviations of the variables included in the regressions for the 3,896 firm-year observations from 1993-2003. All statistics are calculated from the sample pooled across 11 years.
25
Table 2Average cross-sectional correlations of firm characteristics
rDIVPREM rPEGPREM BETA LGROW LMKVL BP COMPOS DISSEMrPEGPREM 0.682
(11/0)1.00
BETA 0.144(8/0)
0.279(11/0)
1.000
LGROW 0.287(11/0)
0.653(11/0)
0.316(11/0)
1.000
LMKVL -0.231(0/11)
-0.321(0/11)
-0.046(0/3)
-0.134(0/8)
1.000
BP 0.135(9/0)
0.237(11/0)
-0.075(0/4)
-0.108(0/7)
-0.365(0/11)
1.00
COMPOS 0.117(9/0)
0.146(8/0)
-0.062(1/4)
-0.025(3/3)
-0.187(0/7)
0.267(10/0)
1.00
DISSEM 0.090(10/0)
0.171(10/0)
0.083(2/0)
0.119(9/0)
-0.793(0/11)
0.239(8/0)
0.127(6/0)
1.00
RPRECIS -0.068(0/4)
-0.121(0/9)
0.042(3/0)
0.038(3/0)
0.180(7/0)
-0.291(0/10)
-0.359(0/11)
-0.115(0/6)
a rDIVPREM is the estimated risk premium based on the target price method (BP 2005). rPEGPREM is the estimated risk premium based on the PEG method (Easton 2004). BETA is capital market beta estimated via the market model with a minimum of 30 monthly returns over the 60 months prior to June 30th of the year expected cost of equity capital is estimated using a value weighted NYSE/AMEX market index return. GROW is the Value Line long-range earnings growth forecasts. MKVL is the market value of equity as of the most recent quarter prior to the date cost of equity is calculated, stated in millions of dollars. BP is the book value of common equity scaled by the market value of common equity, both measured at the end of the most recent quarter prior to June 30th of the year cost of equity capital is estimated. COMPOS is the proportion of overall precision attributed to private information measured as PRIVATE/(PUBLIC + PRIVATE), where PUBLIC is the precision of analysts’ public information set and PRIVATE is the precision of analysts’ private information set, both based on the BKLS method. DISSEM is the dissemination of private information across traders measured the number of informed traders (μ), scaled by the sum of the informed and uninformed traders (μ+2), drawn from the calculation of PIN (EEOW (2001)). PRECIS is total information precision calculated as PUBLIC + PRIVATE. The table contains the time-series means of annual bivariate rank correlations of the variables included in the regressions for the 3,896 firm-year observations from 1993-2003. The numbers in parentheses are the number of years (out of eleven) that the annual correlation coefficient is significantly positive/negative.
26
Table 3Time-series averages of the coefficients in 11 annual cross-sectional regressions (1993-2003).
Panel A: Regressions using rDIVPREM (estimated risk premium based on the target price method) as the proxy for risk.
BETA(+)
LGROW(+)
LMKVL(-)
BP(+)
COMPOS(+)
DISSEM(-)
RPRECIS(-)
Avg. Adj. R2
0.017(4.56)**
0.037(9.76)**
-0.018(-3.40)**
0.007(0.88)
0.007(2.17)*
-0.121(-2.96)**
-0.010(-3.69)**
21.0%
Panel B: Regressions using rPEGPREM (estimated risk premium based on the PEG method) as the proxy for risk.
BETA(+)
LGROW(+)
LMKVL(-)
BP(+)
COMPOS(+)
DISSEM(-)
RPRECIS(-)
Avg. Adj. R2
0.006(3.95)**
0.049(10.85)**
-0.006(-3.74)**
0.022(3.97)**
0.007(5.57)**
-0.038(-2.98)**
-0.014(-3.25)**
59.2%
The sample includes 3,896 firm-year observations from 1993-2003. The t-statistics are based on the standard error of the weighted coefficient estimates across the 11 years (Fama and MacBeth 1973). In calculating the t-statistics, the coefficients are weighted by the square root of the annual sample size to adjust for differences in the number of observations on a year-by-year basis and adjusted for autocorrelation in the annual coefficients
based on an AR(1) autocorrelation structure. Standard errors are multiplied by an adjustment factor, , where n is the number
of years (11) and is the first-order autocorrelation of the annual coefficient estimates (Abarbanell and Bernard, 2000). The dependent variable in Panel A is the estimated risk premium based on the target price method (BP 2005) (rDIVPREM). The dependent variable in Panel B is the estimated risk premium based on the PEG method (Easton 2004) (rPEGPREM). BETA is capital market beta estimated via the market model with a minimum of 30 monthly returns over the 60 months prior to June 30th of the year expected cost of equity capital is estimated using a value weighted NYSE/AMEX market index return. LGROW is natural log of the Value Line long-range earnings growth forecasts. LMKVL is the natural log of the market value of equity as of the most recent quarter prior to the date cost of equity is calculated. BP is the book value of common equity scaled by the market value of common equity, both measured at the end of the most recent quarter prior to June 30th of the year cost of equity capital is estimated. COMPOS is the proportion of overall precision attributed to private information measured as PRIVATE/(PUBLIC + PRIVATE), where PUBLIC is the precision of analysts’ public information set and PRIVATE is the precision of analysts’ private information set, both based on the BKLS method. DISSEM is the dissemination of private information across traders measured the number of informed traders (μ), scaled by the sum of the informed and uninformed traders (μ+2), drawn from the calculation of PIN (EEOW (2001)). RPRECIS is the fractional rank of total information precision calculated as PUBLIC + PRIVATE. T-values are given in parentheses.** (*) denotes significant at the 0.01 (0.05) level or better, < (1-tailed t-test).
27
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2 The figures quoted in the text are from the rPEGPREM regression. The corresponding figures from the rDIVPREM
regression are 7 basis points (for COMPOS), 121 basis points (for DISSEM), and 100 basis points (for RPRECIS).
5 We make appropriate adjustments for fractions of years and the portion of the current fiscal-year dividend forecast
distributed to investors prior to the forecast date. Botosan and Plumlee (2005) describe these adjustments in detail.
6 We eliminate 36 observations from our sample because long- range growth in earnings is in excess of 100%. In
each case, period two forecasted earnings per share is small and negative and the long-range earnings per share is
relatively large and positive. Our conclusions are not altered if these observations are included in our analyses,
although we ultimately eliminate several of the 36 observations as they are influential observations in the
regressions.
8 The form of the log likelihood function we estimate is given in EEOW (2001). It is
9 BP estimate rDIV using three alternative points in the target price range (the 50th percentile, the 25th percentile, and
the minimum value) and find their results are robust to all. BP employ rDIV estimated with the 25th percentile value in
their primary tests to reduce the magnitude of the average estimate; we employ the 50th percentile because doing so
maximizes our sample size.
3 EO also conclude that the existence of some information (even if it is all private) yields a lower cost of equity
capital than no information at all. We do not investigate the fourth prediction since some information exists for all of
the firms included in our analysis.
10 Mean (median) values for μ and (the components of DISSEM) are 88.7 (60.1) and 128.5 (67.5), respectively.
These values are greater than the mean values documented in Brown et al. (2001) (mean μ = 34.5 and mean =46.9)
and Easley, et al. (2002) (mean μ = 31.1 and mean =24.0). Our higher values are consistent with our estimation
31
method, which truncates observations with a large number of buys and sells to a lesser extent, and with a more
recent sample period characterized by greater trade volume. Our sample period ends in 2003, while the Brown et al.
and Easley et al. sample periods end in 1996 and 1998, respectively.
32